computeR {MCARtest}

A function computing the incompatibility index for sequences of correlation matrices

Description

A function solving a SDP problem to compute the incompatibility index R() for a sequence of correlation matrices, as defined in Bordino and Berrett (2024). Writes the SDP problem in standard primal form, and uses csdp to solve this.

Usage

computeR(patterns = list(), SigmaS = list())

Arguments

patterns

A vector with all the patterns in \mathbb{S}

SigmaS

The sequence of correlation matrices \Sigma_\mathbb{S}

Value

The value of R(), in the interval [0,1].

The optimal X_\mathbb{S} for the primal problem.

The sequence of matrices X_\mathbb{S}^{0} as defined in Bordino and Berrett (2024).

The optimal \Sigma for the dual problem.

The sequence of correlation matrices \Sigma_\mathbb{S} in input.

References

Bordino A, Berrett TB (2024). “Tests of Missing Completely At Random based on sample covariance matrices.” arXiv preprint arXiv:2401.05256.

Examples

d = 3

SigmaS=list() #Random 2x2 correlation matrices (necessarily consistent)
for(j in 1:d){
x=runif(2,min=-1,max=1); y=runif(2,min=-1,max=1)
SigmaS[[j]]=cov2cor(x%*%t(x) + y%*%t(y))
}

result = computeR(list(c(1,2),c(2,3), c(1,3)), SigmaS = SigmaS)
result$R